Transcript Strong CP violation in hot QCD : from heavy ion collisions

Winter Workshop on Nuclear Dynamics, La Jolla, 2006
Strong CP violation in hot QCD:
from heavy ion collisions to cosmology
D. Kharzeev
BNL
Phys.Lett.B633 (2006) 260,
+ work in progress
QCD and the UA(1) problem
Invariant under chiral Left
Right
transformations in the limit of massless quarks
UL(Nf)xUR(Nf) chiral symmetry
parity doubling in
the hadron spectrum (not seen!)
If.i broken spontaneously, Nf2 = 9 Goldstone bosons.
Only 8 exist; the ninth, h’ is heavier than the proton!
=> Something is wrong with the flavor-singlet UA(1)…
Axial anomaly
Consider the flavor singlet current
It is not conserved even in the m -> 0 limit due to quantum effects:
Divergence can be written down as
a surface term, and so is seemingly irrelevant:
Instantons
and the UA(1) problem
But: sometimes, surface terms are important
Instantons: classical Euclidean solutions of QCD which map
color SU(2) onto the sphere S3;
in Minkowski space, describe
quantum tunneling between
degenerate vacua with different
topological Chern-Simons numbers
QuickTime™and a
TIFF(Uncompressed) decompressor
are needed to see this picture.
As a result, chiral charge
is no longer conserved
QCD vacuum as a Bloch crystal
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
“q - vacuum”
“quasi-momentum” “coordinate”
The lost symmetries of QCD
The prescription
with the “Bloch” weight
is equivalent to adding to
the Lagrangian a new piece
which is odd under
P, T, CP symmetries !
The strong CP problem
Unless q=0, P, T and CP invariances are lost!
Experiment:
(e.d.m. of
the neutron)
Why q is so small?
Axions?
- PVLAS -recent
Will assume q=0 for the rest of the talk
evidence?
The strong CP problem
and the structure of QCD vacuum
Vafa-Witten theorem: P and CP cannot be broken
spontaneously in QCD
But: 1. it does not constrain metastable states
2. it does not apply at finite temperature,
finite baryon density,
finite isospin density
CP-odd domains in heavy ion collisions:
how to look for them?
DK,
Pisarski,
Tytgat
‘98
v.e.v. of the h field is equivalent to non-zero q
Diffusion of Chern-Simons number in QCD:
real time lattice simulations
DK, A.Krasnitz and R.Venugopalan,
Phys.Lett.B545:298-306,2002
P.Arnold and G.Moore,
Phys.Rev.D73:025006,2006
What are the experimental signatures?
What are the observable signatures of
strong CP violation?
rotate all CP violating phase into the quark piece of the Lagrangian:
is a complex mass parameter
In a CP-odd domain,
This leads to the asymmetry between “left” and “right” quarks
What is “left” and what is “right”? Quarks are massive,
so the definition of chirality depends on the frame…
Azimuthal anisotropy:
collective flow of strongly interacting matter
Hydro limit
STAR
PHOBOS
Description in terms of relativistic hydrodynamics
Quark-gluon plasma: more fluid than water?
A.Nakamura and S.Sakai,
hep-lat/0406009
Superfluid
helium
KSS bound:
strongly coupled SUSY QCD = classical supergravity
Azimuthal anisotropy = angular momentum
What happens if
a superfluid is rotated?
Magnetic vortices in rotating super-fluids
E.J. Yarmchuk, M.J.V. Gordon, and
R.E. Packard,
Observation of Stationary Vortex
Arrays in Rotating Superfluid Helium,
Phys. Rev. Lett. 43, 214 (1979).
J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W.
Ketterle, Observation of Vortex Lattices in Bose-Einstein
Condensates, Science 292, 476 (2001).
Magnetic vortices
“Higgs” field
Energy density
Magnetic vortices in QCD superfluid
and CP violation
Right
anti-quarks
E
Left
quarks
Pz
Fluctuation of chromo-electric field in the presence
of chromo-magnetic vortex produces left quarks and
right anti-quarks (level crossing at the 0th Landau level)
Magnetic vortices in QCD superfluid
and CP violation
Left quarks: in the electric field, energy increases:
Decreases by the same amount for right anti-quarks.
Density of states = longitudinal x transverse:
Rate of chirality generation:
Analogous to cosmic
strings, except not 1D
Magnetic vortices in QCD superfluid
and CP violation
The Fermi momentum has to be smaller than
the mass of the quark in the fluid:
otherwise, energetically unfavorable - quark
can escape into the fluid
(no CP violation for massless quarks!)
What is M in a strongly coupled fluid?
Magnetic vortices in QCD superfluid
and CP violation
Analogs:
Magnetic monopole - induced baryon decay
Cosmic strings
Chirality generation in superfluid 3He
…………
Charge asymmetry w.r.t. reaction plane
as a signature of strong CP violation
excess of positive
charge
+
-
excess of negative
charge
Electric dipole moment of QCD matter!
Charge asymmetry w. r.t. reaction plane
violates T, P, and (by CPT theorem) CP:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Analogy to P violation in weak interactions
Charge asymmetry w.r.t. reaction plane:
how to detect it?
+
-
m
k
S.Voloshin, hep-ph/0406311
Expect
Do we see strong CP violation?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
I. Selyuzhenkov et al., STAR Coll., nucl-ex/0510069; October 25, 2005
Need to analyze the systematics and to understand if the effect is real
Other signatures?
I. Separation of baryon number with respect to reaction plane?
Protons and anti-protons
II. Other observables composed of pion momenta?
Chern-Simons number of chiral fields
III. Lambda helicity correlations?
…
J. Sandweiss
What are the implications for
the Early Universe?
What is the origin of
cosmic magnetic fields?
Magnetic fields are abundant
in the Universe at large scales:
3 mG field in Milky Way;
1-40 mG fields in
clusters of galaxies
Magnetic field in M51:
Polarization of emission
Beck 2000
What is the origin of magnetic fields
in the Universe?
Primordial magnetic field (E.Fermi, 1949)?
Dynamo in proto-galaxy? Stars? Galaxy?
Domain walls and vortices associated with
the q-vacua carry magnetic field;
(“magnetic helicity”,…)
Primordial magnetic field generation at
the QCD phase transition?
Baryons in the Universe
Baryons in the Universe are rare:
1 baryon per ~ 2 billions photons in
the Cosmic Microwave Background Radiation
~ 400 photons/cm3
~ 1 proton/m3
(Almost) no visible antimatter - why the asymmetry?
What is the origin
of the matter-antimatter asymmetry
in the Universe?
1. B violation
2. CP violation
3. Non-equilibrium
dynamics
A.D. Sakharov,
JETP Lett. 5 (1967) 24
QuickTime™ and a
TIFF (Uncompressed) decompressor
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Baryon asymmetry in the Universe
and strong CP violation
1. Generation of Chern-Simons number at the QCD phase transition
is analogous to baryon number generation in the electroweak
phase transition
e.g. V.Kuzmin, V.Rubakov and M.Shaposhnikov,
Phys.Lett.B155(1985)36
2. Strong CP violation
separation of matter
and antimatter in the Universe at the QCD phase transition ?
Summary
1. P and CP violation in hot QCD is not forbidden
2. “All what is not forbidden is allowed” and may exist;
a specific dynamical mechanism - magnetic vortices
3. Rejecting or confirming the signal of P and CP violation
at RHIC is an urgent problem of fundamental importance